Abstract
The asymptotic equilibrium of differential systems in Euclidean spaces has been considered by several authors. These papers deal with a majorant function,g(t, u), which is either non-decreasing or non-increasing inu for eacht. In extending these results to differential systems in a Banach space additional conditions must be placed on the system. In this paper the Kuratowski measure of non-compactness is used to give conditions yielding asymptotic equilibrium of the system in a Banach space.
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Mitchell, A.R., Mitchell, R.W. Asymptotic equilibrium of ordinary differential systems in a Banach space. Math. Systems Theory 9, 308–314 (1975). https://doi.org/10.1007/BF01735148
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DOI: https://doi.org/10.1007/BF01735148